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Maximizing bichromatic reverse nearest neighbor for L p -norm in two- and three-dimensional spaces

Abstract

Bichromatic reverse nearest neighbor (BRNN) has been extensively studied in spatial database literature. In this paper, we study a related problem called MaxBRNN: find an optimal region that maximizes the size of BRNNs for L p -norm in two- and three- dimensional spaces. Such a problem has many real-life applications, including the problem of finding a new server point that attracts as many customers as possible by proximity. A straightforward approach is to determine the BRNNs for all possible points that are not feasible since there are a large (or infinite) number of possible points. To the best of our knowledge, there are no existing algorithms which solve MaxBRNN for any L p -norm space of two- and three-dimensionality. Based on some interesting properties of the problem, we come up with an efficient algorithm called MaxOverlap for to solve this problem. Extensive experiments are conducted to show that our algorithm is efficient.

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References

  1. 1

    Amato, N.M., Goodrich, M., Ramos, E.A.: Computing the arrangement of curve segments: Divide-and-conquer algorithms via sampling. In: Proceedings of the 11th ACM-SIAM Symposium on Discreate Algorithms, pp. 705–706 (2000)

  2. 2

    Beckmann, N., Kriegel, H.-P., Schneider, R., Seeger, B.: The R*-tree: an efficient and robust access method for points and rectangles. In: Proceedings of the ACM SIGMOD International Conference on Management of Data, pp. 322–331 (1990)

  3. 3

    Cabello S., Diaz-Banex J.M., Langerman S., Seara C.: Facility location problems in the plane based on reverse nearest neighbor queries. Eur. J. Operat. Res. 202(1), 99–106 (2010)

    MATH  Article  Google Scholar 

  4. 4

    Cabello, S., Diaz-Banez, J.M., Langerman, S., Seara, C., Ventura, I.: Reverse facility location problems. In: Canadian Conference on Computational Geometry, pp. 68–71 (2005)

  5. 5

    Cardinal, J., Langerman, S.: Min-max-min geometric facility location problems. In: 22nd European Workshop on Computational Geometry (2006)

  6. 6

    Chazelle B.: Filtering search: a new approach to query-answering. SIAM J. Comput. 15, 703–724 (1986)

    MathSciNet  MATH  Article  Google Scholar 

  7. 7

    Chazelle B.: New upper bounds for neighbor searching. Inf. Control 68(1–3), 105–124 (1986)

    MathSciNet  MATH  Article  Google Scholar 

  8. 8

    Chiueh, T.: Content-based image indexing. In: VLDB (1994)

  9. 9

    de Berg M., van Kreveld M., Overmars M., Schwarzkopf O.: Computational Geometry: Algorithms and Applications. Springer, Berlin (2000)

    MATH  Google Scholar 

  10. 10

    Du, Y., Zhang, D., Xia, T.: The optimal-location query. In: SSTD, pp. 163–180 (2005)

  11. 11

    Kang, J.M., Mokbel, M.F., Shekhar, S., Xia, T., Zhang, D.: Continuous evaluation of monochromatic and bichromatic reverse nearest neighbors. In: Proceedings of the International Conference on Data Engineering, pp. 806–815 (2007)

  12. 12

    Korn, F., Muthukrishnan, S.: Influence sets based on reverse nearest neighbor queries. In: Proceedings of the ACM SIGMOD International Conference on Management of Data, pp. 201–212 (2000)

  13. 13

    Krarup J., Pruzan P.M.: The simple plant location problem: survey and synthesis. Eur. J. Operat. Res. 12(1), 36–57 (1983)

    MathSciNet  MATH  Article  Google Scholar 

  14. 14

    Shahabi C., Kolahdouzan M.R., Sharifzadeh M.: A road network embedding technique for k-nearest neighbor search in moving object databases. GeoInformatica 7(3), 255–273 (2003)

    Article  Google Scholar 

  15. 15

    Stanoi, I., Riedewald, M., Agrawal, D., Abbadi, A.E.: Discovery of influence sets in frequently updated databases. In: Proceedings of the International Conference on Very Data Bases (VLDB). (2001)

  16. 16

    Tansel B.C., Francis R.L., Lowe T.: Location on networks: a survey. Manage. Sci. 29(4), 482–497 (1983)

    MathSciNet  MATH  Article  Google Scholar 

  17. 17

    Tao Y., Faloutsos C., Papadias D.: Spatial query estimation without the local uniformity assumption. GeoInformatica 10(3), 261–293 (2006)

    Article  Google Scholar 

  18. 18

    Yiu, L.H.U.M.L., Mouratidis, K., Mamoulis, N.: Capacity constrained assignment in spatial databases. In: Proceedings of the ACM SIGMOD International Conference on Management of Data, pp. 15–28 (2008)

  19. 19

    Wong, R.C.-W., Ozsu, T., Fu, A.W.-C., Yu, P.S., Liu, L., Liu, Y.: Maximizing bichromatic reverse nearest neighbor for lp-norm in two- and three-dimensional spaces. In: http://www.cse.ust.hk/~raywong/paper/maxRNNtechnicalReport.pdf(2011)

  20. 20

    Wong, R.C.-W., Ozsu, T., Yu, P.S., Fu, A.W.-C.: Efficient method for maximizing bichromatic reverse nearest neighbor. In: Proceedings of the International Conference on Very Data Bases (VLDB). (2009)

  21. 21

    Wong, R.C.-W., Tao, Y., Fu, A.W.-C., Xiao, X.: On efficient spatial matching. In: Proceedings of the International Conference on Very Data Bases (VLDB), pp. 579–590 (2007)

  22. 22

    Xia, T., Zhang, D., Kanoulas, E., Du, Y.: On computing top-t most influential spatial sites. In: Proceedings of the International Conference on Very Data Bases (VLDB), pp. 946–957 (2005)

  23. 23

    Zhang, D., Du, Y., Xia, T., Tao, Y.: Progressive computation of the min-dist optimal-location query. In: Proceedings of the International Conference on Very Data Bases (VLDB), pp. 643–654 (2006)

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Correspondence to Raymond Chi-Wing Wong.

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This is an extended version of the paper that appeared in the International Conference on Very Large Databases, 2009.

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Wong, R.CW., Özsu, M.T., Fu, A.WC. et al. Maximizing bichromatic reverse nearest neighbor for L p -norm in two- and three-dimensional spaces. The VLDB Journal 20, 893–919 (2011). https://doi.org/10.1007/s00778-011-0230-1

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Keywords

  • Spatial databases
  • Indexing
  • Reverse nearest neighbor